Chapter 4 Control, Functions, and Classes

June 7, 1999 10:10 owltex Sheet number 17 Page number 99 magenta black

Control, Functions, and Classes 4

If A equals success, then the formula is A = X + Y + Z. X is work. Y is play. Z is keep your mouth shut. Albert Einstein quoted in SIGACT News, Vol. 25, No. 1, March 1994

Your “if” is the only peacemaker; much virtue in “if.” William Shakespeare As You Like It, V, iv

Leave all else to the gods. Horace Odes, Book I, Ode ix

In the programs studied in Chapter 3, statements executed one after the other to produce output. This was true both when all statements were in main or when control was transferred from main to another function, as it was in SlicePrice in pizza.cpp, Program 3.5. However, code behind the scenes in gﬂy.cpp, Program 3.6, executed differently in response to the user’s input and to a simulated wind-shear effect. Many programs require nonsequential control. For example, transactions made at automatic teller machines (ATMs) process an identiﬁcation number and present you with a screen of choices. The program controlling the ATM executes different code depending on your choice—for example, either to deposit money or to get cash. This type of control is called selection: a different code segment is selected and executed based on interaction with the user or on the value of a program variable. Another type of program control is repetition: the same sequence of C++ statements is repeated, usually with different values for some of the variables in the statements. For example, to print a yearly calendar your program could call a PrintMonth function twelve times: PrintMonth("January", 31); //... PrintMonth("November",30); PrintMonth("December",31); Here the name of the month and the number of days in the month are arguments passed to PrintMonth. Alternatively, you could construct the PrintMonth function to determine the name of the month as well as the number of days in the month given the year and the number of the month. This could be done for the year 2000 by repeatedly executing the following statement and assigning values of 1, 2,...,12 to month: PrintMonth(month, 2000);

99 June 7, 1999 10:10 owltex Sheet number 18 Page number 100 magenta black

100 Chapter 4 Control, Functions, and Classes

In this chapter we’ll study methods for controlling how the statements in a program are executed and how this control is used in constructing functions and classes. To do this we’ll expand our study of arithmetic operators, introduced in the last chapter, to include operators for other kinds of data. We’ll also study C++ statements that alter the ﬂow of control within a program. Finally, we’ll see how functions and classes can be used as a foundation on which we’ll continue to build as we study how programs are used to solve problems. At the end of the chapter you’ll be able to write the function PrintMonth but you’ll also see a class that encapsulates the function so you don’t have to write it.

4.1 The Assignment Operator

In the next three sections we’ll use a program that makes change using U.S. coins to study relational and assignment statements and conditional execution. We’ll use the same program as the basis for what could be a talking cash register. A run of change.cpp, Program 4.1, shows how change is made using quarters, dimes, nickels, and pennies. The program shows how values can be stored in variables using the assignment operator, =. In previous programs the user entered values for variables, but values can also be stored using the assignment operator. The code below assigns values for the circumference and area of a circle according to the radius’ value, then prints the values.1 double radius, area, circumference; cout << "enter radius: "; cin >> radius; area = 3.14159*radius*radius; circumference = 3.14159*2*radius; cout << "area="<> amount;

// calculate number of quarters, dimes, nickels, pennies

quarters = amount/25; amount = amount − quarters∗25;

dimes = amount/10; amount = amount − dimes∗10;

nickels = amount/5; amount = amount − nickels∗5;

pennies = amount;

// output phase of program

cout << "# quarters =\t" << quarters << endl; cout << "# dimes =\t" << dimes << endl; cout << "# nickels =\t" << nickels << endl; cout << "# pennies =\t" << pennies << endl;

return 0; } change.cpp June 7, 1999 10:10 owltex Sheet number 20 Page number 102 magenta black

102 Chapter 4 Control, Functions, and Classes

int amount; int amount;

87 amount = amount - quarters*25; 12 87 - 3*25 Before execution After execution int quarters; 3

Figure 4.1 Updating a variable via assignment.

OUTPUT

prompt> change make change in coins for what amount: 87 # quarters = 3 # dimes = 1 # nickels = 0 # pennies = 2 prompt> change make change in coins for what amount: 42 # quarters = 1 # dimes = 1 # nickels = 1 # pennies = 2

The statement amount = amount - quarters*25 updates the value of the variable amount. The right-hand side of the statement is evaluated ﬁrst. The value of this expression, amount - quarters*25, is stored in the variable on the left- hand side of the assignment statement—that is, the variable amount. This process is diagrammed in Fig. 4.1 when amount is 87. A sequence of assignments can be chained together in one statement:

x=y=z=13;

This statement assigns the value 13 to the variables x, y, and z. The statement is interpreted as x = (y = (z = 13)). The value of the expression (z = 13) is 13, the value assigned to z. This value is assigned to y, and the result of the assignment to y is 13. This result of the expression (y = 13) is then assigned to x. Parentheses aren’t needed in the statement x=y=z=13, because the assignment operator = is right-associative: in the absence of parentheses the rightmost = is evaluated ﬁrst. June 7, 1999 10:10 owltex Sheet number 21 Page number 103 magenta black

4.2 Choices and Conditional Execution 103

Table 4.1 Escape sequences in C++

escape sequence name ASCII \n newline NL (LF) \t horizontal tab HT \v vertical tab VT \b backspace BS \r carriage return CR \f form feed FF \a alert (bell) BEL \\ backslash \ \? question mark ? \’ single quote (apostrophe) ’ \" double quote "

In contrast, the subtraction operator is left-associative, so the expression 8-3-2 is equal to 3, because it is evaluated as (8-3)-2rather than 8-(3-2): here the leftmost subtraction is evaluated ﬁrst. Most operators are left-associative; the associativity of all C++ operators is shown in Table A.4 in Howto A.

Escape Sequences. The output of change.cpp is aligned using a tab character ’\t’. The tab character prints one tab position, ensuring that the amounts of each kind of coin line up. The backslash and t to print the tab character are an example of an escape sequence. Common escape sequences are given in Table 4.1. The table is repeated as Table A.5 in Howto A. Each escape sequence prints a single character. For example, the following statement prints the four-character string "\’".

cout << "\"\\\’\"" << endl;

4.2 Choices and Conditional Execution

I shall set forth from somewhere, I shall make the reckless choice Robert Frost The Sound of the Trees

In this section we’ll alter Program 4.1 so that it only prints the coins used in giv- ing change. We’ll also move the output part of the program to a separate function. By parameterizing the output and using a function, we make it simpler to incorporate modiﬁcations to the original program. June 7, 1999 10:10 owltex Sheet number 22 Page number 104 magenta black

104 Chapter 4 Control, Functions, and Classes

Program Tip 4.1: Avoid duplicating the same code in several places in the same program. Programs will be modiﬁed. If you need to make the same change in more than one place in your code it is very likely that you will leave some changes out, or make the changes inconsistently. In many programs more time is spent in program maintenance than in program development. Often, moving duplicated code to a function and calling the function several times helps avoid code duplication.

Program 4.2 change2.cpp

#include #include using namespace std;

// make change in U.S. coins // Owen Astrachan, 03/17/99

void Output(string coin, int amount) { if (amount > 0) { cout << "# " << coin << " =\t" << amount << endl; } }

int main() { int amount; int quarters, dimes, nickels, pennies;

// input phase of program

cout << "make change in coins for what amount: "; cin >> amount;

// calculate number of quarters, dimes, nickels, pennies

quarters = amount/25; amount = amount − quarters∗25;

dimes = amount/10; amount = amount − dimes∗10;

nickels = amount/5; amount = amount − nickels∗5;

pennies = amount;

// output phase of program

Output("quarters",quarters); Output("dimes",dimes); June 7, 1999 10:10 owltex Sheet number 23 Page number 105 magenta black

4.2 Choices and Conditional Execution 105

Output("nickels",nickels); Output("pennies",pennies);

return 0; } change2.cpp

OUTPUT

prompt> change2 make change in coins for what amount: 87 # quarters = 3 # dimes = 1 # pennies = 2

In the function Output an if statement is used for conditional execution—that is, if makes the execution depend on the value of amount. In the C++ statement

if (amount > 0) { cout << "# " << coin << " =\t" << amount << endl; }

the test expression (amount > 0) controls the cout << statement so that output appears only if the value of the int variable amount is greater than zero.

4.2.1 The if/else Statement An if statement contains a test expression and a body: a group of statements within curly braces { and }. These statements are executed only when the test expression, also called a condition or a guard, is true. The test must be enclosed by parentheses. In the next section we’ll explore op- Syntax: if statement erators that can be used in tests, if ( test expression ) including <, <=, >, and >=. The { body of the if statement can con- statement list; tain any number of statements. } The curly braces that are used to delimit the body of the if statement aren’t needed when there’s only one statement in the body, but we’ll always use them as part of a defensive programming strategy designed to ward off bugs before they appear. June 7, 1999 10:10 owltex Sheet number 24 Page number 106 magenta black

106 Chapter 4 Control, Functions, and Classes

Program 4.3 shows that an if statement can have an else part, which also controls, or guards, a body of statements within curly braces { and } that is executed when the test expression is false. Any kind of statement can appear in the body of an if/else statement, including other if/else Syntax: if/else statement statements. We’ll discuss format- if ( test expression ) ting conventions for writing such { code after we explore the other statement list; kinds of operators that can be used } in the test expressions that are else part of if statements. You may { ﬁnd yourself writing code with statement list; an empty if or else body: one } with no statements. This can always be avoided by changing the test used with the if using rules of logic we’ll discuss in Section 4.7. In Program 4.3, if the value of response is something other than "yes", then the cout << statements associated with the if section are not executed, and the statements in the else section of the program are executed instead. In particular, if the user enters "yeah" or "yup", then the program takes the same action as when the user enters "no". Furthermore, the answer "Yes" is also treated like the answer "no" rather than "yes", because a capital letter is different from the equivalent lower-case letter. As we saw in Program 4.1, change.cpp, the rules of C++ do not require an else section for every if.

Program 4.3 broccoli.cpp

#include #include using namespace std;

// illustrates use of if-else statement

int main() { string response; cout << "Do you like broccoli [yes/no]> "; cin >> response; if ("yes" == response) { cout << "Green vegetables are good for you" << endl; cout << "Broccoli is good in stir-fry as well" << endl; } else { cout << "De gustibus non disputandum" << endl; cout << "(There is no accounting for taste)" << endl; } return 0; } broccoli.cpp June 7, 1999 10:10 owltex Sheet number 25 Page number 107 magenta black

4.3 Operators 107

OUTPUT

prompt> broccoli Do you like broccoli [yes/no]> yes Green vegetables are good for you Broccoli is good in stir-fry as well

prompt> broccoli Do you like broccoli [yes/no]> no De gustibus non disputandum (There is no accounting for taste)

The else section in Program 4.3 could be removed, leaving the following: int main() { string response; cout << "Do you like broccoli [yes/no]> "; cin >> response; if ("yes" == response) { cout << "Green vegetables are good for you" << endl; cout << "Broccoli is good in stir-fry as well" << endl; } return 0; } In this modiﬁed program, if the user enters any string other than "yes", nothing is printed.

ProgramTip 4.2: Use an if statement to guard a sequence of statements and an if/else statement to choose between two sequences. The if statement solves the problem of guarding the sequence of statements in the body of the if so that these statements are executed only when a certain condition holds. The if/else statement solves the problem of choosing between two different sequences. Later in the chapter we’ll see how to choose between more than two sequences using cascaded if/else statements.

4.3 Operators

We’ve seen arithmetic operators such as +, *, %, the assignment operator =, and the < operator used in if/else statements. In this section we’ll study the other operators available in C++. You’ll use all these operators in constructing C++ programs. June 7, 1999 10:10 owltex Sheet number 26 Page number 108 magenta black

108 Chapter 4 Control, Functions, and Classes

Table 4.2 The relational operators

symbol meaning example == equal to if ("yes" == response) > greater than if (salary > 30000) < less than if (0 < salary) != not equal to if ("yes" != response) >= greater than or equal to ≥ if (salary >= 10000) <= less than or equal to ≤ if (20000 <= salary)

4.3.1 Relational Operators

Comparisons are odious. John Fortescue De Laudibus Legum Angliae, 1471

The expressions that form the test of an if statement are built from different operators. In this section we’ll study the relational operators, which are used to determine the relationships between different values. Relational operators are listed in Table 4.2. The parenthesized expression that serves as the test of an if statement can use any of the relational operators shown in Table 4.2. The parenthesized expressions evaluate to true or false and are called boolean expressions, after the mathematician George Boole. Boolean expressions have one of two values: true or false. In C++ programs, any nonzero value is considered “true,” and zero-valued expressions are considered “false.” The C++ type bool is used for variables and expressions with one of two values: true and false. Although bool was ﬁrst approved as part of C++ in 1994, some older compilers do not support it.2 We’ll use true and false as values rather than zero and one, but remember that zero is the value used for false in C++ . The relational operators < and > behave as you might expect when used with int and double values. In the following statement the variable salary can be an int or a double. In either case the phrase about minimum wage is printed if the value of salary is less than 10.0.

2If you’re using a compiler that doesn’t support bool as a built-in type, you can use the header ﬁle bool.h supplied with the code from this book via #include"bool.h" to get access to a programmer-deﬁned version of type bool. June 7, 1999 10:10 owltex Sheet number 27 Page number 109 magenta black

4.3 Operators 109

if (salary < 10.0) { cout << "you make below minimum wage" << endl; }

When string values are compared, the behavior of the inequality operators < and > is based on a dictionary order, sometimes called lexicographical order:

string word; cout << "enter a word: "; cin >> word; if (word < "middle") { cout << word << " comes before middle" << endl; }

In the foregoing code fragment, entering the word "apple" generates the following output. OUTPUT

apple comes before middle

Entering the word "zebra" would cause the test (word < "middle") to evaluate to false, so nothing is printed. The comparison of strings is based on the order in which the strings would appear in a dictionary, so that "A" comes before "Z". Sometimes the behavior of string comparisons is unexpected. Entering "Zebra", for example, generates this output: OUTPUT

Zebra comes before middle

This happens because capital letters come before lower-case letters in the ordering of characters used on most computers.3 To see how relational operators are evaluated, consider the output of these statements:

cout << (13 < 5) << endl; cout << (5+1<6*2)<

3We’ll explore the ASCII character set, which is used to determine this ordering, in Chapter 9. June 7, 1999 10:10 owltex Sheet number 28 Page number 110 magenta black

110 Chapter 4 Control, Functions, and Classes

OUTPUT

0 1

The value of 13<5is false, which is zero; and the value of 6<12is true, which is one. (In Howto B, a standard method for printing bool values as true and false, rather than 1 and 0, is shown.) In the last output statement, the arithmetic operations are executed ﬁrst, because they have higher precedence than relational operators. You’ve seen precedence used with arithmetic operators; for example, multiplication has higher precedence than addition, so that 3 + 4 × 2 = 11. You can use parentheses to bypass the normal precedence rules. The expression (3 + 4) × 2 evaluates to 14 rather than 11. A table showing the relative precedence of all C++ operators can be found in Table A.4 in Howto A.

Program Tip 4.3: When you write expressions in C++ programs, use parentheses liberally. Trying to uncover precedence errors in a complex expression can be very frustrating. Looking for precedence errors is often the last place you’ll look when trying to debug a program. As part of defensive programming, use parentheses rather than relying exclusively on operator precedence.

Because execution of an if statement depends only on whether the test is true or false (nonzero or zero), the following code is legal in C++ :

if(6+3-9) { cout << "great minds think alike" << endl; } else { cout << "fools seldom differ" << endl; }

These statements cause the string “fools seldom differ” to be output, because the expression (6 + 3 − 9) evaluates to 0, which is false in C++ . Although this code is legal, it is not necessarily good code. It is often better to make the comparison explicit, as in

if (x != 0) { DoSomething(); }

rather than relying on the equivalence of “true” and any nonzero value:

if (x) { DoSomething(); } June 7, 1999 10:10 owltex Sheet number 29 Page number 111 magenta black

4.3 Operators 111

which is equivalent in effect, but not in clarity. There are situations, however, in which the second style of programming is clearer. When such a situation arises, I’ll point it out.

4.3.2 Logical Operators As we will see (for example, in usemath.cpp, Program 4.6, it can be necessary to check that a value you enter is in a certain range (e.g., not negative). In change.cpp, Program 4.1, the program should check to ensure that the user’s input is valid (e.g., between 0 and 99). The following code implements this kind of check. if (choice < 0) { cout << "illegal choice" << endl; } else if (choice > 99) { cout << "illegal choice" << endl; } else { // choice ok, continue } This code has the drawback of duplicating the code that’s executed when the user enters an illegal choice. Suppose a future version of the program will require the user to reenter the choice. Modifying this code fragment would require adding new code in two places, making the likelihood of introducing an error larger. In addition, when code is duplicated, it is often difﬁcult to make the same modiﬁcations everywhere the code appears. Logical operators allow boolean expressions to be combined, as follows: if (choice<0||choice > 99) { cout << "illegal choice" << endl; } else { // choice ok, continue } The test now reads, “If choice is less than zero or choice is greater than ninety-nine.” The test is true (nonzero) when either choice < 0 or choice > 99. The operator || is the logical or operator. It evaluates to true when either or both of its boolean arguments is true. The logical and operator && operates on two boolean expressions and returns true only when both are true. The preceding test for valid input can be rewritten using logical and as follows: if (0 <= choice && choice <= 99) { // choice ok, continue } else { cout << "illegal choice" << endl; } June 7, 1999 10:10 owltex Sheet number 30 Page number 112 magenta black

112 Chapter 4 Control, Functions, and Classes

Table 4.3 Truth table for logical operators

A B A||B A&&B !A false false false false true false true true false true true false true false false true true true true false

Be careful when translating English or mathematics into C++ code. The phrase “choice is between 0 and 99” is often written in mathematics as 0 ≤ choice ≤ 99. In C++, relational operators are left-associative, so the following if test, coded as it would be in mathematics, will evaluate to true for every value of choice. if (0 <= choice <= 99) { // choice ok, continue } Since the leftmost <= is evaluated ﬁrst (the relational operators, like all binary operators, are left associative), the test is equivalent to ( (0 <= choice) <= 99 ) and the value of the expression (0 <= choice) is either false (0) or true (1), both of which are less than or equal to 99, thus satisfying the second test. There is also a unary operator ! that works with boolean expressions. This is the logical not operator. The value of !expression is false if the value of expression is true, and true when the value of expression is false. The two expressions below are equivalent. x != y !(x == y) Because ! has a very high precedence, the parentheses in the expression on the right are necessary (see Table A.4).

4.3.3 Short-Circuit Evaluation The following statement is designed to print a message when a grade-point average is higher than 90%: if (scoreTotal/numScores > 0.90) { cout << "excellent! very good work" << endl; } This code segment might cause a program to exit abnormally4 if the value of numScores is zero, because the result of division by zero is not deﬁned. The abnormal exit can be avoided by using another nested if statement (the approach required in languages such as Pascal):

4The common phrase for such an occurrence is bomb, as in “The program bombed.” If you follow good defensive programming practices, your programs should not bomb. June 7, 1999 10:10 owltex Sheet number 31 Page number 113 magenta black

4.3 Operators 113

if (numScores != 0) { if (scoreTotal/numScores > 0.90) { cout << "excellent! very good work" << endl; } }

However, in languages like C, C++, and Java another approach is possible: if (numScores != 0 && scoreTotal/numScores > 0.90) { cout << "excellent! very good work" << endl; }

The subexpressions in an expression formed by the logical operators && and || are evaluated from left to right. Furthermore, the evaluation automatically stops as soon as the value of the entire test expression can be determined. In the present example, if the expression numScores != 0 is false (so that numScores is equal to 0), the entire expression must be false, because when && is used to combine two boolean subexpressions, both subexpressions must be true (nonzero) for the entire expression to be true (see Table 4.3). When numScores == 0, the expression scoreTotal/numScores > 0.90 will not be evaluated, avoiding the potential division by zero. Similarly, when || is used, the second subexpression will not be evaluated if the ﬁrst is true, because in this case the entire expression must be true—only one subexpression needs to be true for an entire expression to be true with ||. For example, in the code if (choice<1||choice > 3) { cout << "illegal choice" << endl; }

the expression choice > 3 is not evaluated when choice is 0. In this case, choice <1is true, so the entire expression must be true. The term short-circuit evaluation describes this method of evaluating boolean expressions. The short circuit occurs when some subexpression is not evaluated because the value of the entire expression is already determined. We’ll make extensive use of short-circuit evaluation (also called “lazy evaluation”) in writing C++ programs.

4.3.4 Arithmetic Assignment Operators C++ has several operators that serve as “contractions,” in the grammatical sense that “I’ve” is a contraction of “I have.” These operators aren’t necessary, but they can simplify and shorten code that changes the value of a variable. For example, several statements in change.cpp, Program 4.1, alter the value of amount; these statements are similar to the following: amount = amount - quarters*25;

This statement can be rewritten using the operator -=. amount -= quarters*25; June 7, 1999 10:10 owltex Sheet number 32 Page number 114 magenta black

114 Chapter 4 Control, Functions, and Classes

Table 4.4 Arithmetic assignment operators.

symbol example equivalent += x+=1; x=x+1; *= doub *= 2; doub = doub * 2; -= n-=5; n=n-5; /= third /= 3; third = third / 3; %= odd %= 2; odd = odd % 2;

Similarly, the statement number = number + 1, which increments the value of number by one, can be abbreviated using the += operator: number += 1;.In general, the statement variable = variable + expression; has exactly the same effect as the statement variable += expression; Using such assignment operators can make programs easier to read. Often a long variable name appearing on both sides of an assignment operator = will cause a lengthy expression to wrap to the next line and be difﬁcult to read. The arithmetic assignment operators summarized in Table 4.4 can alleviate this problem. It’s not always possible to use an arithmetic assignment operator as a contraction when a variable appears on both the left and right sides of an assignment statement. The variable must occur as the ﬁrst subexpression on the right side. For example, if x has the value zero or one, the statement x=1-xchanges the value from one to zero and vice versa. This statement cannot be abbreviated using the arithmetic assignment operators.

4.4 Block Statements and Defensive Programming

Following certain programming conventions can lead to programs that are more under- standable (for you and other people reading your code) and more easily developed. In this book we follow the convention of using block delimiters, { and }, for each part of an if/else statement. This is shown in change2.cpp, Program 4.2. It is possible to write the if statement in Program 4.2 without block delimiters: if (amount > 0) cout << "# " << coin << " =\t" << amount << endl; The test of the if statement controls the output statement so that it is executed only when amount is greater than zero. As we’ve seen, it is useful to group several statements together so that all are executed precisely when the test of an if/else statement is true. To do this, a block (or compound) statement is used. A block statement is a sequence of one or more statements enclosed by curly braces, as shown in Program 4.2. If no braces are used, a program may compile and run, but its behavior might be other than expected. Consider the following program fragment: June 7, 1999 10:10 owltex Sheet number 33 Page number 115 magenta black

4.4 Block Statements and Defensive Programming 115

int salary; cout << "enter salary "; cin >> salary; if (salary > 30000) cout << salary << " is a lot to earn " << endl; cout << salary*0.55 << " is a lot of taxes << endl; cout << "enter \# of hours worked "; ...

Two sample runs of this fragment follow:

OUTPUT

enter salary 31000 31000 is a lot to earn 17050.00 is a lot of taxes enter # of hours worked … enter salary 15000 8250.00 is a lot of taxes enter # of hours worked …

Stumbling Block Note that the indentation of the program fragment might suggest to someone reading the program (but not to the compiler!) that the “lot of taxes” message should be printed only when the salary is greater than 30,000. However, the taxation message is always printed. The compiler interprets the code fragment as though it were written this way:

int salary; cout << "enter salary "; cin >> salary; if (salary > 30000) { cout << salary << " is a lot to earn " << endl; } cout << salary*0.55 << " is a lot of taxes " << endl; cout << "enter # of hours worked ";

When 15000 is entered, the test salary > 30000 evaluates to false, and the statement about “a lot to earn” is not printed. The statement about a “lot of taxes”, however, is printed, because it is not controlled by the test. Indentation and spacing are ignored by the compiler, but they are important for people reading and developing programs. For this reason, we will always employ braces {} and a block statement when using if/else statements, even if the block statement consists of only a single statement. June 7, 1999 10:10 owltex Sheet number 34 Page number 116 magenta black

116 Chapter 4 Control, Functions, and Classes

4.4.1 Defensive Programming Conventions

This convention of always using braces is an example of a defensive programming strategy: writing code to minimize the potential for causing errors. Suppose you decide to add another statement to be controlled by the test of an if statement that is initially written without curly braces. When the new statement is added, it will be necessary to include the curly braces that delimit a block statement, but that is easy to forget to do. Since the missing braces can cause a hard-to-detect error, we adopt the policy of including them even when there is only a single statement controlled by the test.

ProgramTip 4.4: Adopt coding conventions that make it easier to modify programs. You’ll rarely get a program right the first time. Once a program works correctly, it’s very likely that you’ll need to make modifications so that the program works in contexts unanticipated when first designed and written. More time is spent modifying programs than writing them first, so strive to make modification as simple as possible.

Program 4.4 noindent.cpp

#include #include using namespace std; int main() { string response; cout << "Do you like C++ programming [yes/no]> "; cin >> response; if ("yes" == response) { cout << "It's more than an adventure, it can be a job" << endl; } else { cout << "Perhaps in time you will" << endl; } return 0;} noindent.cpp

In this book the left curly brace { always follows an if/else on the next line after the line on which the if or else occurs. The right curly brace } is indented the same level as the if/else to which it corresponds. Other indentation schemes are possible; one common convention follows, this is called K&R style after the originators of C, Kernighan and Ritchie.

if ("yes" == response) { cout << "Green vegetables are good for you" << endl; cout << "Broccoli is good in stir-fry as well" << endl; }

You can adopt either convention, but your boss (professor, instructor, etc.) may require a certain style. If you’re consistent, the particular style isn’t that important, although it’s often the cause of many arguments between supporters of different indenting styles. June 7, 1999 10:10 owltex Sheet number 35 Page number 117 magenta black

4.4 Block Statements and Defensive Programming 117

In this book we usually include the ﬁrst statement between curly braces on the same line as the ﬁrst (left) brace. If you use this style of indenting, you will not press return after you type the left curly brace {. However, we sometimes do press return, which usually makes programs easier to read because of the extra white space5. To see that indentation makes a difference, note that noindent.cpp, Program 4.4, compiles and executes without error but that no consistent indentation style is used. Notice that the program is much harder for people to read, although the computer “reads” it with no trouble.

Stumbling Block Problems with = and ==. Typing = when you mean to type == can lead to hard-to-locate bugs in a program. A coding convention outlined here can help to alleviate these bugs, but you must keep the distinction between = and == in mind when writing code. Some compilers are helpful in this regard and issue warnings about “potentially unintended assignments.” The following program fragment is intended to print a message depending on a person’s age: string age; cout << "are you young or old [young/old]: "; cin >> age; if (age = "young") { cout << "not for long, time flies when you’re having fun"; } else { cout << "hopefully you’re young at heart"; } If the user enters old, the message beginning “not for long…” is printed. Can you see why this is the case? The test of the if/else statement should be read as “if age gets young.” The string literal "young" is assigned to age, and the result of the assignment is nonzero (it is "young", the value assigned to age). Because anything nonzero is regarded as true, the statement within the scope of the if test is executed. You can often prevent such errors by putting constants on the left of comparisons as follows: if ("young" == age) // do something If the assignment operator is used by mistake, as in if ("young" = age), the compiler will generate an error.6 It is much better to have the compiler generate an error message than to have a program with a bug in it. Putting constants on the left in tests is a good defensive programming style that can help to trap potential bugs and eliminate them before they creep into your programs.

5In a book, space is more of a premium than it is on disk—hence the style of indenting that does not use the return. You should make sure you follow the indenting style used by your boss, supervisor, or programming role model. 6On one compiler the error message “error assignment to constant” is generated. On another, the less clear message “sorry, not implemented: initialization of array from dissimilar array type” is generated. June 7, 1999 10:10 owltex Sheet number 36 Page number 118 magenta black

118 Chapter 4 Control, Functions, and Classes

4.4.2 Cascaded if/else Statements Sometimes a sequence of if/else statements is used to differentiate among several possible values of a single expression. Such a sequence is called cascaded. An example is shown in monthdays.cpp, Program 4.5.

Program 4.5 monthdays.cpp

#include #include using namespace std;

// illustrates cascaded if/else statements

int main() { string month; int days = 31; // default value of 31 days/month

cout << "enter a month (lowercase letters): "; cin >> month;

// 30 days hath september, april, june, and november

if ("september" == month) { days = 30; } else if ("april" == month) { days = 30; } else if ("june" == month) { days = 30; } else if ("november" == month) { days = 30; } else if ("february" == month) { days = 28; } cout << month << " has " << days << " days" << endl;

return 0; } monthdays.cpp

It’s possible to write the code in monthdays.cpp using nested if/else statements as follows. This results in code that is much more difﬁcult to read than code using cascaded if/ else statements. Whenever a sequence of if/else statements like this is used to test the value of one variable repeatedly, we’ll use cascaded if/else statements. The rule of using a block statement after an else is not (strictly speaking) followed, but the code is much easier to read. Because a block statement follows the if, we’re not violating the spirit of our coding convention. June 7, 1999 10:10 owltex Sheet number 37 Page number 119 magenta black

4.4 Block Statements and Defensive Programming 119

if ("april" == month) { days = 30; } else { if ("june" == month) { days = 30; } else { if ("november" == month) { days = 30; } else { if ("february" == month) { days = 28; } } } }

OUTPUT

prompt> days4 enter a month (lowercase letters): january january has 31 days prompt> days4 enter a month (lowercase letters): april april has 30 days prompt> days4 enter a month (lowercase letters): April April has 31 days

Pause to Reﬂect 4.1 The statements altering amount in change.cpp, Program 4.1, can be written using the mod operator %.Ifamount = 38, then amount/25 == 1, and amount %25==13, which is the same value as 38 - 25*1. Rewrite the program using the mod operator. Try to use an arithmetic assignment operator. 4.2 Describe the output of Program 4.3 if the user enters the string "Yes", the string "yup", or the string "none of your business". 4.3 Why is days given a “default” value of 31 in monthdays.cpp, Program 4.5? June 7, 1999 10:10 owltex Sheet number 38 Page number 120 magenta black

120 Chapter 4 Control, Functions, and Classes

4.4 How can monthdays.cpp, Program 4.5, be modiﬁed to take leap years into account? 4.5 Modify broccoli.cpp, Program 4.3, to include an if statement in the else clause so that the “taste” lines are printed only if the user enters the string "no". Thus you might have lines such as

if ("yes" == response) { } else if ("no" == response) { }

4.6 Using the previous modiﬁcation, add a ﬁnal else clause (with no if statement) so that the output might be as follows:

OUTPUT

prompt> broccoli Do you like broccoli [yes/no]> no De gustibus non disputandum (There is no accounting for good taste) prompt> broccoli Do you like broccoli [yes/no]> nope Sorry, only responses of yes and no are recognized

4.7 Write a sequence of if/else statements using > and, perhaps, < that prints a message according to a grade between 0 and 100, entered by the user. For example, high grades might get one message and low grades might get another message. 4.8 Explain why the output of the ﬁrst statement below is 0, but the output of the second is 45:

cout << (9*3<4*5)<

Why are the parentheses needed? 4.9 What is output by each of the following statements (why?)

cout << (9*5<45) <

4.4 Block Statements and Defensive Programming 121

4.10 Write a code fragment in which a string variable grade is assigned one of three states: "High Pass", "Pass", and "Fail" according to whether an input integer grade is between 80 and 100, between 60 and 80, or below 60, respectively. It may be useful to write the fragment so that a message is printed and then modify it so that a string variable is assigned a value.

Stumbling Block The Dangling Else Problem. Using the block delimiters { and } in all cases when writing if/else statements can prevent errors that are very difﬁcult to ﬁnd because the indentation, which conveys meaning to a reader of the program, is ignored by the compiler when code is generated. Using block delimiters also helps in avoiding a problem that results from a potential ambiguity in computer languages such as C++ that use if/else statements (C and Pascal have the same ambiguity, for example). The following code fragment attempts to differentiate odd numbers less than zero from other numbers. The indentation of the code conveys this meaning, but the code doesn’t execute as intended: if(x%2==1) if (x < 0) cout << " number is odd and less than zero" << endl; else cout << " number is even " << endl;

What happens if the int object x has the value 13? The indentation seems to hint that nothing will be printed. In fact, the string literal "number is even" will be printed if this code segment is executed when x is 13. The segment is read by the compiler as though it is indented as follows: if(x%2==1) if (x < 0) cout << " number is odd and less than zero" << endl; else cout << " number is even " << endl;

The use of braces makes the intended use correspond to what happens. Nothing is printed when x has the value 13 in if(x%2==1) { if(x<0) cout << " number is odd and less than zero" << endl; } else { cout << " number is even " << endl; }

As we have noted before, the indentation used in a program is to assist the human reader. The computer doesn’t require a consistent or meaningful indentation scheme. Misleading indentation can lead to hard-to-ﬁnd bugs where the human sees what is intended rather than what exists. June 7, 1999 10:10 owltex Sheet number 40 Page number 122 magenta black

122 Chapter 4 Control, Functions, and Classes

One rule to remember from this example is that an else always corresponds to the most recent if. Without this rule there is ambiguity as to which if the else belongs; this is known as the dangling-else problem. Always employ curly braces { and } when using block statements with if/else statements (and later with looping constructs). If braces are always used, there is no ambiguity, because the braces serve to delimit the scope of an if test.

Claude Shannon (b. 1916)

Claude Shannon founded information theory—a subfield of computer science that is used today in developing methods for encrypting information. Encryption is used to store data in a secure manner so that the information can be read only by designated people. In his 1937 master’s thesis, Shannon laid the foundation on which modern computers are built by equating Boolean logic with electronic switches. This work en- abled hardware designers to design, build, and test circuits that could perform logical as well as arithmetic operations. In an interview in [Hor92], Shannon responds to the comment that his thesis is “possibly the most important master’s thesis in the cen- tury” with “It just happened that no one else was familiar with both those fields at the same time.” He then adds a wonderful non sequitur: “I’ve always loved that word ‘Boolean.’ ” Shannon is fond of juggling and riding unicycles. Among his inven- tions are a juggling “dummy” that looks like W.C. Fields and a computer THROBAC: Thrifty Roman Numeral Backward Computer. Although much of Shannon’s work has led to significant advances in the theory of communication, he says: I’ve always pursued my interests without much regard for financial value or the value to the world; I’ve spent lots of time on totally useless things. Shannon’s favorite food is vanilla ice cream with chocolate sauce. Shannon received the National Medal of Science in 1966. For more information see [Sla87, Hor92]. June 7, 1999 10:10 owltex Sheet number 41 Page number 123 magenta black

4.5 Functions That ReturnValues 123

Calling function sqrt(115.0) double value; 115.0 cin >> value; double cout << ... << sqrt(value) << endl; sqrt(double x) 115.0 ... { double root; } // code to give root a value return root; }

cin >> value; Returning 10.7238 from sqrt(115.0) cout << ... << 10.7238 << endl; ... }

Figure 4.2 Evaluating the function call sqrt115.0

4.5 FunctionsThat ReturnValues

Civilization advances by extending the number of important operations which we can perform without thinking about them. Alfred North Whitehead An Introduction to Mathematics

In Chapter 3 we studied programmer-deﬁned functions, such as SlicePrice in pizza.cpp, Program 3.5, whose prototype is

void SlicePrice(int radius, double price)

The return type of SlicePrice is void. Many programs require functions that have other return types. You’ve√ probably seen mathematical functions on hand-held calcula- tors such as sin(x) or x. These functions are different from the function SlicePrice in that they return a value. For example, when you use a calculator, you√ might enter the number 115, then press the square-root key. This displays the value of 115 or 10.7238. The number 115 is an argument to the square root function. The value returned by the function is the number 10.7238. Program 4.6 is a C++ program that processes information in the same way: users enter a number, and the square root of the number is displayed. Control ﬂow from usemath.cpp is shown in Fig. 4.2. The value 115, entered by the user and stored in the variable value, is copied into a memory location associated with the parameter x in the function sqrt. The square root of 115 is calculated, and a return statement in the function sqrt returns this square root, which is used in place of the expression sqrt(value) in the cout statement. As shown in Fig. 4.2, the value 10.7238 is displayed as a result. June 7, 1999 10:10 owltex Sheet number 42 Page number 124 magenta black

124 Chapter 4 Control, Functions, and Classes

The function sqrt is accessible by including the header file . Table 4.5 lists some of the functions accessible from this header file. A more complete table of functions is given as Table F.1 in Howto F. In the sample output of usemath.cpp, √Program 4.6, the square roots of floating-point numbers aren’t always exact. For example, 100.001 = 10.0000499998, but the value displayed is 10. Floating-point values cannot always be exactly determined. Because of inherent limits in the way these values are stored in the computer, the values are rounded off to the most precise values that can be represented in the computer. The resulting roundoff error illustrates the theme of conceptual and formal models introduced in Chapter 1. Conceptually, the square root of 100.001 can be calculated with as many decimal digits as we have time or inclination to write down. In the formal model of floating-point numbers implemented on computers, the precision of the calculation is limited.

Program 4.6 usemath.cpp

#include #include using namespace std;

// illustrates use of math function returning a value

int main() { double value; cout << "enter a positive number "; cin >> value; cout << "square root of " << value <<"="<

return 0; } usemath.cpp

OUTPUT

prompt> usemath enter a positive number 115 square root of 115 = 10.7238 prompt> usemath enter a positive number 100.001 square root of 100.001 = 10 prompt> usemath enter a positive number -16 square root of -16 = nan June 7, 1999 10:10 owltex Sheet number 43 Page number 125 magenta black

4.5 Functions That ReturnValues 125

Table 4.5 Some functions in

function name prototype returns double fabs (double x) absolute value of x double log (double x) natural log of x double log10 (double x) base-ten log of x double sin (double x) sine of x (x in radians) double cos (double x) cosine of x (x in radians) double tan (double x) tangent of x (x in radians) double asin (double x) arc sine of x [−π/2,π/2] double acos (double x) arc cosine of x [0,π] double atan (double x) arc tangent of x [−π/2,π/2] double pow (double x, xy double y) √ double sqrt (double x) x, square root of x double floor (double x) largest integer value ≤ x double ceil (double x) smallest integer value ≥ x

Finally, although the program prompts for positive numbers, there is no check to ensure that the user has entered a positive number. In the output shown, the symbol nan stands for “not a number.”7 Not all compilers will display this value. In particular, on some computers, trying to take the square root of a negative number may cause the machine to lock up. It would be best to guard the call sqrt(value) using an if statement such as the following one: if (0 <= value) { cout << "square root of " << value <<"=" << sqrt(value) << endl; } else { cout << "nonpositive number " << value << " entered" << endl; } Alternatively, we could compose the function sqrt with the function fabs, which computes absolute values. cout << "square root of " << value <<"=" << sqrt(fabs(value)) << endl; The result returned by the function fabs is used as an argument to sqrt. Since the return type of fabs is double (see Table 4.5), the argument of sqrt has the right type.

7Some compilers print NaN, others crash rather than printing an error value. June 7, 1999 10:10 owltex Sheet number 44 Page number 126 magenta black

126 Chapter 4 Control, Functions, and Classes

4.5.1 The Math Library In C and C++ several mathematical functions are available by accessing a math library using #include .8 Prototypes for some of these functions are listed in Table 4.5, and a complete list is given as Table F.1 in Howto F. All of these functions return double values and have double parameters. Integer values can be converted to doubles, so the expression sqrt(125) is legal (and evaluates to 11.18033). The function pow is particularly useful, because there is no built-in exponentiation operator in C++. For example, the statement cout << pow(3,13) << endl} outputs the value of 313: three to the thirteenth. The functions declared in are tools that can be used in any program. As programmers, we’ll want to develop functions that can be used in the same way. On occasion, we’ll develop functions that aren’t useful as general-purpose tools but make the development of one program simpler. For example, in pizza.cpp, Program 3.5, the price per square inch of pizza is calculated and printed by the function SlicePrice. If the value were returned by the function rather than printed, it could be used to determine which of several pizzas was the best buy. This is shown in pizza2.cpp, Pro- gram 4.7. Encapsulating the calculation of the price per square inch in a function, as opposed to using the expression smallPrice/(3.14159 * smallRadius * smallRadius), avoids errors that might occur in copying or retyping the expression for a large pizza. Using a function also makes it easier to include other sizes of pizza in the same program. If it develops that we’ve made a mistake in calculating the price per square inch, isolating the mistake in one function makes it easier to change than ﬁnding all occurrences of the calculation and changing each one.

Program 4.7 pizza2.cpp

#include using namespace std;

// find the price per square inch of pizza // to compare large and small sizes for the best value // // Owen Astrachan // March 29, 1999 //

double Cost(double radius, double price) // postcondition: returns the price per sq. inch { return price/(3.14159∗radius∗radius); }

8The name cmath is the C++ math library, but with many older compilers you will need to use math.h rather than cmath. June 7, 1999 10:10 owltex Sheet number 45 Page number 127 magenta black

4.5 Functions That ReturnValues 127

int main() { double smallRadius, largeRadius; double smallPrice, largePrice; double smallCost,largeCost;

// input phase of computation

cout << "enter radius and price of small pizza "; cin >> smallRadius >> smallPrice;

cout << "enter radius and price of large pizza "; cin >> largeRadius >> largePrice;

// process phase of computation

smallCost = Cost(smallRadius,smallPrice); largeCost = Cost(largeRadius,largePrice);

// output phase of computation

cout << "cost of small pizza="<

if (smallCost < largeCost) { cout << "SMALL is the best value " << endl; } else { cout << "LARGE is the best value " << endl; }

return 0; } pizza2.cpp

OUTPUT

prompt> pizza2 enter radius and price of small pizza 6 6.99 enter radius and price of large pizza 8 10.99 cost of small pizza = 0.0618052 per sq.inch cost of large pizza = 0.0546598 per sq.inch LARGE is the best value

From the user’s point of view, Program 3.5 and Program 4.7 exhibit similar, though not identical, behavior. When two programs exhibit identical behavior, we describe this sameness by saying that the programs are identical as black boxes. We cannot see the June 7, 1999 10:10 owltex Sheet number 46 Page number 128 magenta black

128 Chapter 4 Control, Functions, and Classes

inside of a black box; the behavior of the box is discernible only by putting values into the box (running the program) and noting what values come out (are printed by the program). A black box speciﬁes input and output, but not how the processing step takes place. The balloon class and the math function sqrt are black boxes; we don’t know how they are implemented, but we can use them in programs by understanding their input and output behavior.

4.5.2 Pre- and Post-conditions In the function SlicePrice of pizza2.cpp, Program 4.7, a comment is given in the form of a postcondition. A postcondition of a function is a statement that is true when the function ﬁnishes executing. Each function in this book will include a postcondition that describes what the function does. Some functions have preconditions. A precondition states what parameter values can be passed to the function. Together a function’s precondition and postcondition provide a contract for programmers who call the function: if the precondition is true the postcondition will be true. For example, a precondition of the function sqrt might be that the function’s parameter is non-negative.

Program Tip 4.5: When calling functions, read postconditions carefully. When writing functions, provide postconditions. When possible, provide a precondition as well as a postcondition since preconditions provide programmers with information about what range of values can be passed to each parameter of a function.

In the main function of pizza2.cpp, the extraction operator >> extracts two values in a single statement. Just as the insertion operator << can be used to put several items on the output stream cout, the input stream cin continues to ﬂow so that more than one item can be extracted.

Pause to Reflect 4.11 Write program fragments or complete programs that convert degrees Celsius to degrees Fahrenheit, British thermal units (Btu) to joules (J), and knots to miles per hour. Note that x degrees Celsius equals (9/5)x + 32 degrees Fahrenheit; that x J equals 9.48 × 10−4(x)Btu; and that 1 knot = 101.269 ft/min (and that 5,280 ft = 1 mile). At first do this without using assignment statements, by incorporating the appropriate expressions in output statements. Then define variables and use assignment statements as appropriate. Finally, write functions for each of the conversions. 4.12 Modify pizza2.cpp, Program 4.7, to use the function pow to square radius in the function Cost. 4.13 If a negative argument to the function sqrt causes an error, for what values of x does the following code fragment generate an error?

if (x >= 0 && sqrt(x) > 100) cout << "big number" << endl; June 7, 1999 10:10 owltex Sheet number 47 Page number 129 magenta black

4.5 Functions That ReturnValues 129

4.14 Heron’s formula gives the area of a triangle in terms of the lengths of the sides of the triangle: a, b, and c. p area = s · (s − a) · (s − b) · (s − c) (4.1) where s is the semiperimeter, or half the perimeter a + b + c of the triangle. Write a function TriangleArea that returns the area of a triangle. The sides of the triangle should be parameters to TriangleArea. 4.15 The law of cosines gives the length of one side of a triangle, c, in terms of the other sides a and b and the angle C formed by the sides a and b: c2 = a2 + b2 − 2 · a · b cos (C)

Write a function SideLength that computes the length of one side of a triangle, given the other two sides and the angle (in radians) between the sides as parameters to SideLength. 4.16 The following code fragment allows a user to enter three integers: int a,b,c; cout << "enter three integers "; cin>>a>>b>>c; Add code that prints the average of the three values read. Does it make a difference if the type is changed from int to double? Do you think that >> has the same kind of associativity as =, the assignment operator?

4.5.3 Function ReturnTypes The functions sqrt and SlicePrice used in previous examples both returned double values. In this section we’ll see that other types can be returned.

Determining Leap Years. Leap years have an extra day (February 29) not present in nonleap years. We use arithmetic and logical operators to determine whether a year is a leap year. Although it’s common to think that leap years occur every four years, the rules for determining leap years are somewhat more complicated, because the period of the Earth’s rotation around the Sun is not exactly 365.25 days but approximately 365.2422 days.

If a year is evenly divisible by 400, then it is a leap year. Otherwise, if a year is divisible by 100, then it is not a leap year. The only other leap years are evenly divisible by 4.9

9These rules correspond to a year length of 365.2425 days. In the New York Times of January 2, 1996 (page B7, out-of-town edition), a correction to the rules used here is given. The year 4000 is not a leap year, nor will any year that’s a multiple of 4000 be a leap year. Apparently this rule, corresponding to a year length of 365.24225 days, will have to be modiﬁed too, but we probably don’t need to worry that our program will be used beyond the year 4000. June 7, 1999 10:10 owltex Sheet number 48 Page number 130 magenta black

130 Chapter 4 Control, Functions, and Classes

For example, 1992 is a leap year (it is divisible by 4), but 1900 is not a leap year (it is divisible by 100), yet 2000 is a leap year, because, although it is divisible by 100, it is also divisible by 400. The boolean-valued function IsLeapYear in Program 4.8 uses multiple return statements to implement this logic. Recall that in the expression (a%b)the modulus operator % evaluates to the remainder when a is divided by b. Thus, 2000 % 400 == 0, since there is no remainder when 2000 is divided by 400. The sequence of cascaded if statements in IsLeapYear tests the value of the parameter year to determine whether it is a leap year. Consider the ﬁrst run shown, when year has the value 1996. The ﬁrst test, year % 400 == 0, evaluates to false, because 1996 is not divisible by 400. The second test evaluates to false, because 1996 is not divisible by 100. Since 1996 = 4 × 499, the third test, (year%4==0),is true, so the value true is returned from the function IsLeapYear. This makes the expression IsLeapYear(1996) in main true, so the message is printed indicating that 1996 is a leap year. You may be tempted to write if (IsLeapYear(year) == true)

rather than using the form shown in isleap.cpp. This works, but the true is redundant, because the function IsLeapYear is boolean-valued: it is either true or false. The comments for the function IsLeapYear are given in the form of a precondition and a postcondition. For our purposes, a precondition is what must be satisfied for the function to work as intended. The “as intended” part is what is specified in the postcondition. These conditions are a contract for the caller of the function to read: if the precondition is satisfied, the postcondition will be satisfied. In the case of IsLeapYear the precondition states that the function works for any year greater than 0. The function is not guaranteed to work for the year 0 or if a negative year such as −10 is used to indicate the year 10 B.C. It is often possible to implement a function in many ways so that its postcondition is satisfied. Program 4.9 shows an alternative method for writing IsLeapYear. Us- ing a black-box test, this version is indistinguishable from the IsLeapYear used in Program 4.8.

Program 4.8 isleap.cpp

#include using namespace std;

// illustrates user-defined function for determining leap years

bool IsLeapYear(int year) // precondition: year > 0 // postcondition: returns true if year is a leap year, else returns false { if (year % 400 == 0) // divisible by 400 { return true; } June 7, 1999 10:10 owltex Sheet number 49 Page number 131 magenta black

4.5 Functions That ReturnValues 131

else if (year % 100 == 0) // divisible by 100 { return false; } else if (year%4==0) //divisible by 4 { return true; } return false; }

int main() { int year; cout << "enter a year "; cin >> year; if (IsLeapYear(year)) { cout << year << " has 366 days, it is a leap year" << endl; } else { cout << year << " has 365 days, it is NOT a leap year" << endl; } return 0; } isleap.cpp

OUTPUT

prompt> isleap enter a year 1996 1996 has 366 days, it is a leap year

prompt> isleap enter a year 1900 1900 has 365 days, it is NOT a leap year

Program 4.9 isleap2.cpp

bool IsLeapYear(int year) // precondition: year > 0 // postcondition: returns true if year is a leap year, else false { return (year % 400 == 0) || (year%4==0&&year % 100 != 0 ); } isleap2.cpp

A boolean value is returned from IsLeapYear because the logical operators && and || return boolean values. For example, the expression IsLeapYear(1974) causes the following expression to be evaluated by substituting 1974 for year: June 7, 1999 10:10 owltex Sheet number 50 Page number 132 magenta black

132 Chapter 4 Control, Functions, and Classes

(1974 % 400 == 0) || ( 1974%4==0&&1974 % 100 != 0 );

Since the logical operators are evaluated left to right to support short-circuit evaluation, the subexpression 1974 % 400 == 0 is evaluated first. This subexpression is false, because 1974 % 400 is 374. The rightmost parenthesized expression is then evaluated, and its subexpression 1974%4==0is evaluated first. Since this subexpression is false, the entire && expression must be false (why?), and the expression 1974 % 100 != 0 is not evaluated. Since both subexpressions of || are false, the entire expression is false, and false is returned. Boolean-valued functions such as IsLeapYear are often called predicates. Predi- cate functions often begin with the prefix Is. For example, the function IsEven might be used to determine whether a number is even; the function IsPrime might be used to determine whether a number is prime (divisible by only 1 and itself, e.g., 3, 17); and the function IsPalindrome might be used to determine whether a word is a palindrome (reads the same backward as forward, e.g., mom, racecar).

Program Tip 4.6: Follow conventions when writing programs. Conven- tions make it easier for other people to read and use your programs and for you to read them long after you write them. One common convention is using the preﬁx Is for predicate/boolean-valued functions.

Converting Numbers to English. We’ll explore a program that converts some integers to their English equivalent. For example, 57 is “ﬁfty-seven” and 14 is “fourteen.” Such a program might be the basis for a program that works as a talking cash register, speaking the proper coins to give as change. With speech synthesis becoming cheaper on computers, it’s fairly common to encounter a computer that “speaks.” The number you hear after dialing directory assistance is often spoken by a computer. There are many home ﬁnance programs that print checks; these programs employ a method of converting numbers to English to print the checks. In addition to using arithmetic operators, the program shows that functions can return strings as well as numeric and boolean types, and it emphasizes the importance of pre- and postconditions.

Program 4.10 numtoeng.cpp

#include #include using namespace std;

// converts two digit numbers to English equivalent // Owen Astrachan, 3/30/99

string DigitToString(int num) // precondition: 0 <= num < 10 // postcondition: returns english equivalent, e.g., 1->one,...9->nine June 7, 1999 10:10 owltex Sheet number 51 Page number 133 magenta black

4.5 Functions That Return Values 133

{ if (0 == num) return "zero"; else if (1 == num) return "one"; else if (2 == num) return "two"; else if (3 == num) return "three"; else if (4 == num) return "four"; else if (5 == num) return "five"; else if (6 == num) return "six"; else if (7 == num) return "seven"; else if (8 == num) return "eight"; else if (9 == num) return "nine"; else return "?"; }

string TensPrefix(int num) // precondition: 10 <= num <= 99 and num % 10 == 0 // postcondition: returns ten, twenty, thirty, forty, etc. // corresponding to num, e.g., 50->fifty { if (10 == num) return "ten"; else if (20 == num) return "twenty"; else if (30 == num) return "thirty"; else if (40 == num) return "forty"; else if (50 == num) return "fifty"; else if (60 == num) return "sixty"; else if (70 == num) return "seventy"; else if (80 == num) return "eighty"; else if (90 == num) return "ninety"; else return "?"; }

string TeensToString(int num) // precondition: 11 <= num <= 19 // postcondition: returns eleven, twelve, thirteen, fourteen, etc. // corresponding to num, e.g., 15 -> fifteen { if (11 == num) return "eleven"; else if (12 == num) return "twelve"; else if (13 == num) return "thirteen"; else if (14 == num) return "fourteen"; else if (15 == num) return "fifteen"; else if (16 == num) return "sixteen"; else if (17 == num) return "seventeen"; else if (18 == num) return "eighteen"; else if (19 == num) return "nineteen"; else return "?"; }

string NumToString(int num) // precondition: 0 <= num <= 99 // postcondition: returns english equivalent, e.g., 1->one, 13->thirteen { if (0 <= num && num < 10) { return DigitToString(num); } June 7, 1999 10:10 owltex Sheet number 52 Page number 134 magenta black

134 Chapter 4 Control, Functions, and Classes

else if (10 < num && num < 20) { return TeensToString(num); } else if (num % 10 == 0) { return TensPrefix(num); } else { // concatenate ten’s digit with one’s digit return TensPrefix(10 ∗ (num/10)) + "-" + DigitToString(num % 10); } }

int main() { int number; cout << "enter number between 0 and 99: "; cin >> number; cout << number <<"="<

OUTPUT

prompt> numtoeng enter number between 0 and 99: 22 22 = twenty-two

prompt> numtoeng enter number between 0 and 99: 17 17 = seventeen

prompt> numtoeng enter number between 0 and 99: 103 103 = ?-three

The code in the DigitToString function does not adhere to the rule of using block statements in every if/else statement. In this case, using {} delimiters would make the program unnecessarily long. It is unlikely that statements will be added (necessitating the use of a block statement), and the form used here is clear. June 7, 1999 10:10 owltex Sheet number 53 Page number 135 magenta black

4.5 Functions That ReturnValues 135

Program Tip 4.7: White space usually makes a program easier to read and clearer. Block statements used with if/else statements usually make a program more robust and easier to change. However, there are occasions when these rules are not followed. As you become a more practiced programmer, you’ll develop your own aesthetic sense of how to make programs more readable.

A new use of the operator + is shown in function NumToString. In the ﬁnal else statement, three strings are joined together using the + operator:

return TensPrefix(10*(num/10))+ "-" + DigitToString(num%10);

When used with string values, the + operator joins or concatenates (sometimes “catenates”) the string subexpressions into a new string. For example, the value of "apple" + "sauce" isanewstring, "applesauce". This is another example of operator overloading; the + operator has different behavior for string, double, and int values.

Robust Programs. In the sample runs shown, the final input of 103 does not result in the display of one hundred three. The value of 103 violates the precondition of NumToString, so there is no guarantee that the postcondition will be satisfied. Robust programs and functions do not bomb in this case, but either return some value that indicates an error or print some kind of message telling the user that input values aren’t valid. The problem occurs in this program because "?" is returned by the function call TensPrefix(10 * (num/10)). The value of the argument to TensPrefix is 10×(103/10) == 10×10 == 100. This value violates the precondition of TensPrefix. If no final else were included to return a question mark, then nothing would be returned from the function TensPrefix when it was called with 103 as an argument. This situation makes the concatenation of “nothing” with the hyphen and the value returned by DigitToString(num % 10) problematic, and the program would terminate, because there is no string to join with the hyphen. Many programs like numtoeng.cpp prompt for an input value within a range. A function that ensures that input is in a specific range by reprompting would be very useful. A library of three related functions is specified in prompt.h. We’ll study these functions in the next chapter, and you can find information about them in Howto G. Here is a modified version of main that uses PromptRange:

int main() { int number = PromptRange("enter a number",0,99); cout << number <<"="<

return 0; } June 7, 1999 10:10 owltex Sheet number 54 Page number 136 magenta black

136 Chapter 4 Control, Functions, and Classes

OUTPUT

prompt> numtoeng enter number between 0 and 99: 103 enter a number between 0 and 99: 100 enter a number between 0 and 99: -1 enter a number between 0 and 99: 99 99 = ninety-nine

You don’t have enough programming tools to know how to write PromptRange (you need loops, studied in the next chapter), but the speciﬁcations of each function make it clear how the functions are called. You can treat the functions as black boxes, just as you treat the square-root function sqrt in as a black box.

Pause to Reﬂect 4.17 Write a function DaysInMonth that returns the number of days in a month encoded as an integer with 1 = January, 2 = February,…, 12 = December. The year is needed, because the number of days in February depends on whether the year is a leap year. In writing the function, you can call IsLeapYear. The speciﬁcation for the function is

int DaysInMonth(int month,int year) // pre: month coded as: 1 = january, ..., 12 = december // post: returns # of days in month in year

4.18 Why are parentheses needed in the expression TensPrefix(10*(num/10))? For example, if TensPrefix(10*num/10) is used, the program generates a non-number when the user enters 22.

4.19 Write a predicate function IsEven that evaluates to true if its int parameter is an even number. The function should work for positive and negative integers. Try to write the function using only one statement: return expression.

4.20 Write a function DayName whose header is

string DayName(int day) // pre: 0 <= day <= 6 // post: returns string representing day, with // 0 = "Sunday", 1 = "Monday", ..., 6 = "Saturday"

so that the statement cout << DayName(3) << endl; prints Wednesday.

4.21 Describe how to modify the function NumToString in numtoeng.cpp, Pro- gram 4.10, so that it works with three-digit numbers. June 7, 1999 10:10 owltex Sheet number 55 Page number 137 magenta black

4.6 Class Member Functions 137

4.22 An Islamic year y is a leap year if the remainder, when 11y + 14 is divided by 30, is less than 11. In particular, the 2nd, 5th, 7th, 10th, 13th, 16th, 18th, 21st, 24th, 26th, and 29th years of a 30-year cycle are leap years. Write a function IsIslamicLeapYear that works with this deﬁnition of leap year. 4.23 In the Islamic calendar [DR90] there are also 12 months, which strictly alternate between 30 days (odd-numbered months) and 29 days (even-numbered months), except for the twelfth month, Dhu al-Hijjah, which in leap years has 30 days. Write a function DaysInIslamicMonth for the Islamic calendar that uses only three if statements.

4.6 Class Member Functions

Section 3.4 discusses a class named Balloon for simulating hot-air balloons. We’ve used the class string extensively in our examples, but we haven’t used all of the functionality provided by strings themselves. Recall from Section 3.4 that functions provided by a class are called member functions. In this section we’ll study three string member functions, and many more are explained in Howto C. We’ll also have a sneak preview at the class Date which is covered more extensively in the next chapter. We’ll show just one example program using the class, but the program provides a glimpse of the power that classes bring to programming.

4.6.1 string Member Functions The functions we’ve studied so far, like those in , are called free functions because they do not belong to a class. Member functions are part of a class and are invoked by applying a function to an object with the dot operator. Program 4.11 shows the string member functions length and substr. The function length returns the number of characters in a string, the function substr returns a substring of a string given a starting position and a number of characters.

Program 4.11 strdemo.cpp

#include #include using namespace std;

// illustrates string member functions length() and substr()

int main() { string s; cout << "enter string: "; cin >> s; int len = s.length(); cout << s << " has " << len << " characters" << endl; cout << "first char is " << s.substr(0, 1) << endl; June 7, 1999 10:10 owltex Sheet number 56 Page number 138 magenta black

138 Chapter 4 Control, Functions, and Classes

cout << "last char is " << s.substr(s.length()−1, 1) << endl; cout << endl << "all but first is " << s.substr(1,s.length()) << endl; return 0; } strdemo.cpp

OUTPUT

prompt> strdemo enter string: theater theater has 7 characters first char is t last char is r all but first is heater prompt> strdemo enter string: slaughter theater has 9 characters first char is s last char is r all but first is laughter

The ﬁrst position or index of a character in a string is zero, so the last index in a string of 11 characters is 10. The prototypes for these functions are given in Table 4.6. Each string member function used in Program 4.11 is invoked using an object and the dot operator. For example, s.length() returns the length of s. When I read code, I read this as “s dot length”, and think of the length function as applied to the object s, returning the number of characters in s.

Table 4.6 Three string member functions

function prototype and description int length() postcondition: returns the number of characters in the string

string substr(int pos, int len) precondition: 0 <= pos < length() postcondition: returns substring of len characters beginning at position pos (as many characters as possible if len too large, but error if pos is out of range)

int find(string s) postcondition: returns ﬁrst position/index at which string s begins (returns string::npos if s does not occur) June 7, 1999 10:10 owltex Sheet number 57 Page number 139 magenta black

4.6 Class Member Functions 139

Program Tip 4.8: Ask not what you can do to an object, ask what an object can do to itself. When you think about objects, you’ll begin to think about what an object can tell you about itself rather than what you can tell an object to do.

In the last use of substr in Program 4.11 more characters are requested than can be supplied by the arguments in the call s.substr(1, s.length()). Starting at index 1, there are only s.length()-1 characters in s. However, the function substr “does the right thing” when asked for more characters than there are, and gives as many as it can without generating an error. For a full description of this and other string functions see Howto C. Although the string returned by substr is printed in strdemo.cpp, the returned value could be stored in a string variable as follows: string allbutfirst = s.substr(1,s.length());

The string Member Function find. The member function find returns the index in a string at which another string occurs. For example, "plant" occurs at index three in the string "supplant", at index ﬁve in "transplant", and does not occur in "vegetable". Program 4.12, strﬁnd.cpp shows how find works. The return value string::npos indicates that a substring does not occur. Yourcode should not depend on string::npos having any particular value10.

Program 4.12 strﬁnd.cpp

#include #include using namespace std;

int main() { string target = "programming is a creative process"; string s; cout << "target string: " << target << endl; cout << "search for what substring: "; cin >> s; int index = target.find(s); if (index != string::npos) { cout << "found at " << index << endl; } else { cout << "not found" << endl; } return 0; } strﬁnd.cpp

10Actually, the value of string::npos is the largest positive index, see Howto C. June 7, 1999 10:10 owltex Sheet number 58 Page number 140 magenta black

140 Chapter 4 Control, Functions, and Classes

OUTPUT

prompt> strfind target string: programming is a creative process search for what substring: pro found at 0 prompt> strfind target string: programming is a creative process search for what substring: gram found at 3 prompt> strfind target string: programming is a creative process search for what substring: create not found

The double colon :: used in string::npos separates the value, in this case npos, from the class in which the value occurs, in this case string. The :: is called the scope resolution operator, we’ll study it in more detail in the next chapter.

4.6.2 Calling and Writing Functions When you ﬁrst begin to use functions that return values, you may forget to process the return value. All non-void functions return a value that should be used in a C++ expression (e.g., printed, stored in a variable, used in an arithmetic expression). The following C++ statements show how three of the functions studied in this chapter (sqrt, NumToString, and IsLeap) are used in expressions so that the values returned by the functions aren’t ignored.

double hypotenuse = sqrt{side1*side1 + side2*side2); cout << NumToString(47) << endl; bool millenniumLeaps = IsLeap(2000) || IsLeap(3000);

It doesn’t make sense, for example, to write the following statements in which the value returned by sqrt is ignored.

double s1, s2; cout << "enter sides: "; cin >> s1 >> s2; double root; sqrt(s1*s1 + s2*s2);

The programmer may have meant to store the value returned by the function call to sqrt in the variable root, but the return value from the function call in the last statement is ignored. June 7, 1999 10:10 owltex Sheet number 59 Page number 141 magenta black

4.6 Class Member Functions 141

Whenever you call a function, think carefully about the function’s prototype and its postcondition. Be sure that if the function returns a value that you use the value.11

ProgramTip 4.9: Do not ignore the value returned by non-void functions. Think carefully about each function call you make when writing programs and do something with the return value that makes sense in the context of your program and that is consistent with the type and value returned.

Write Lots of Functions. When do you write a function? You may be writing a program like pizza2.cpp, Program 4.7, where the function Cost is used to calculate how much a square inch of pizza costs. The function is reproduced here. double Cost(double radius, double price) // postcondition: returns the price per sq. inch { return price/(3.14159*radius*radius); } Is it worth writing another function called CircleArea like this? double CircleArea(double radius) // postcondition: return area of circle with given radius { return radius*radius*3.14159; } In general, when should you write a function to encapsulate a calculation or sequence of statements? There is no simple answer to this question, but there are a few guidelines.

Program Tip 4.10: Functions encapsulate abstractions and lead to code that’s often easier to read and modify. Do not worry about so-called execution time “overhead” in the time it takes a program to execute a function call. Make your programs correct and modiﬁable before worrying about making them fast.

As an example, it’s often easier to write a complex boolean expression as a function that might include if/else statements, and then call the function, than to determine what the correct boolean expression is. In the next section we’ll study a tool from logic that helps in writing correct boolean expressions, but writing functions are useful when you’re trying to develop appropriate loop tests. For example, if you need to determine

11Some functions return a value but are called because they cause some change in program state separate from the value returned. Such functions are said to have side-effects since they cause an effect “on the side,” or in addition to the value returned by the function. In some cases the returned value of a function with side-effects is ignored. June 7, 1999 10:10 owltex Sheet number 60 Page number 142 magenta black

142 Chapter 4 Control, Functions, and Classes

if a one-character string represents a consonant, it’s probably easier to write a function IsVowel and use that function to write IsConsonant,ortouse!IsVowel() when you need to determine if a string is a consonant.

bool IsVowel(string s) // pre: s is a one-character string // post: returns true if s is a vowel, return false { if (s.length() != 1) { return false; } return s == "a" || s == "e" || s == "i" || s == "o" || s == "u"; }

The return Statement. In the function IsVowel() there are two return statements and an if without an else. When a return statement executes, the function being returned from immediately exits. In IsVowel(), if the string parameter s has more than one character, the function immediately returns false. Since the function exits, there is no need for an else body, though some programmers prefer to use an else. Some programmers prefer to have a single return statement in every function. To do this requires introducing a local variable and using an else body as follows.

bool IsVowel(string s) // pre: s is a one-character string // post: returns true if s is a vowel, else return false { bool retval = false; // assume false if (s.length() == 1) { retval = (s == "a" || s == "e" || s == "i" || s == "o" || s == "u"); } return retval; }

You should try to get comfortable with the assignment to retval inside the if statement. It’s often easier to think of the assignment using this code.

if (s == "a"|| s == "e"|| s == "i"|| s == "o"|| s == "u") { retval = true; } else { retval = false; }

This style of programming uses more code. It’s just as efﬁcient, however, and it’s ok to use it though the single assignment to retval is more terse and, to many, more elegant. June 7, 1999 10:10 owltex Sheet number 61 Page number 143 magenta black

4.6 Class Member Functions 143

4.6.3 The Date class At the beginning of this chapter we discussed writing a function PrintMonth that prints a calendar for a month specified by a number and a year. As described, printing a calendar for January of the year 2001 could be done with the call PrintMonth(1,2001).You could write this function with the tools we’ve studied in this chapter though it would be cumbersome to make a complete calendar. However, using the class Date makes it much simpler to write programs that involve dates and calendars than writing your own functions like IsLeap. In general, it’s easier to use classes that have been developed and debugged than to develop your own code to do the same thing, though it’s not always possible to find classes that serve your purposes. We won’t discuss this class in detail until the next chapter, but you can see how variables of type Date are defined, and two of the Date member functions used in Program 4.13. More information about the class is accessible in Howto G. To use Date objects you’ll need to add #include"date.h" to your programs.

Program 4.13 datedemo.cpp

#include using namespace std; #include "date.h"

// simple preview of using the class Date

int main() { int month, year; cout << "enter month (1-12) and year "; cin >> month >> year;

Date d(month, 1, year); cout << "that day is " << d << ", it isa"<

return 0; } datedemo.cpp

After examining the program and the output on the next page, you should be think about how you would use the class Date to solve the following problems, each can be solved with just a few lines of code.

Pause to Reﬂect 4.24 Determine if a year the user enters is a leap year.

4.25 Determine the day of the week of any date (month, day, year) the user enters.

4.26 Determine the day of the week your birthday falls on in the year 2002. June 7, 1999 10:10 owltex Sheet number 62 Page number 144 magenta black

144 Chapter 4 Control, Functions, and Classes

OUTPUT

prompt> datedemo enter month (1-12) and year 9 1999 that day is September 1 1999, it is a Wednesday the month has 30 days in it prompt> datedemo enter month (1-12) and year 2 2000 that day is February 1 2000, it is a Tuesday the month has 29 days in it

4.7 Using Boolean Operators: De Morgan’s Law

Many people new to the study of programming have trouble developing correct expressions used for the guard of an if statement. For example, suppose you need to print an error message if the value of an int variable is either 7 or 11.

if (value == 7 || value == 11) { cout << "**error** illegal value: " << value << endl; }

The statement above prints an error message for the illegal values of 7 and 11 only and not for other, presumably legal, values. On the other hand, suppose you need to print an error message if the value is anything other than 7 or 11 (i.e., 7 and 11 are the only legal values). What do you do then? Some beginning programmers recognize the similarity between this and the previous problem and write code like the following.

if (value == 7 || value == 11) { // do nothing, value ok } else { cout << "**error** illegal value: " << value << endl; }

This code works correctly, but the empty block guarded by the if statement is not the best programming style. One simple way to avoid the empty block is to use the logical negation operator. In the code below the operator ! negates the expression that follows so that an error message is printed when the value is anything other than 7 or 11.

if ( ! (value == 7 || value == 11) ) { cout << "**error** illegal value: " << value << endl; } June 7, 1999 10:10 owltex Sheet number 63 Page number 145 magenta black

4.7 Using Boolean Operators: De Morgan’s Law 145

Table 4.7 De Morgan’s Laws for logical operators

expression logical equivalent by De Morgan’s law ! (a && b) (!a) || (!b) ! (a || b) (!a) && (!b)

Alternatively, we can use De Morgan’s law12 to ﬁnd the logical negation, or opposite, of an expression formed with the logical operators && and ||. De Morgan’s laws are summarized in Table 4.7. The negation of an && expression is an || expression, and vice versa. We can use De Morgan’s law to develop an expression for printing an error message for any value other than 7 or 11 by using the logical equivalent of the guard in the if statement above.

if ( (value != 7 && (value != 11) ) { cout << "**error** illegal value: " << value << endl; }

De Morgan’s law can be used to reason effectively about guards when you read code. For example, if the code below prints an error message for illegal values, what are the legal values?

if (s != "rock" && s != "paper" && s != "scissors") { cout << "** error** illegal value: " << s << endl; }

By applying De Morgan’s law twice, we ﬁnd the logical negation of the guard which tells us the legal values (what would be an else block in the statement above.)

if (s == "rock" || s == "paper" || s == "scissors") //legal

This shows the legal values are “rock” or “paper” or “scissors” and all other strings represent illegal values.

12Augustus De Morgan (1806–1871), ﬁrst professor of mathematics at University College, London, as well as teacher to Ada Lovelace (see Section 2.5.2.) June 7, 1999 10:10 owltex Sheet number 64 Page number 146 magenta black

146 Chapter 4 Control, Functions, and Classes

Richard Stallman (b. 1953)

Richard Stallman is hailed by many as “the world’s best programmer.” Before the term hacker became a pejorative, he used it to describe himself as “someone fascinated with how things work, [who would see a broken machine and try to fix it].” Stallman believes that software should be free, that money should be made by adapting software and explaining it, but not by writing it. Of software he says, “I’m go- ing to make it free even if I have to write it all myself.” Stallman uses the analogy that for software he means “free as in free speech, not as in free beer.” He is the founder of the GNU software project, which creates and distributes free software tools. The GNU g++ compiler, used to develop the code in this book, is widely regarded as one of the best compilers in the world. The free operating system Gnu/Linux has become one of the most widely used operating systems in the world. In 1990 Stallman received a MacArthur “ge- nius” award of $240,000 for his dedication and work. He continues this work today as part of the League for Programming Freedom, an organization that fights against software patents (among other things). In an interview after receiving the MacArthur award, Stallman had a few things to say about programming freedom: I disapprove of the obsession with profit that tempts people to throw away their ideas of good citizenship.…businesspeople design software and make their profit by obstructing others’ understanding. I made a decision not to do that. Everything I do, people are free to share. The only thing that makes developing a program worthwhile is the good it does.

4.8 Chapter Review

In this chapter we discussed using and building functions. Changing the ﬂow of control within functions is important in constructing programs. Encapsulating information in functions that return values is an important abstraction technique and a key concept in building large programs. The if/else statement can be used to alter the ﬂow of control in a program. June 7, 1999 10:10 owltex Sheet number 65 Page number 147 magenta black

4.8 Chapter Review 147

You can write programs that respond differently to different inputs by using if/else statements. The test in an if statement uses relational operators to yield a boolean value whose truth determines what statements are executed. In addition to relational operators, logical (boolean), arithmetic, and assignment operators were discussed and used in several different ways. The following C++ and general programming features were covered in this chapter:

The if/else statement is used for conditional execution of code. Cascaded if statements are formatted according to a convention that makes them more readable. A function’s return type is the type of value returned by the function. For example, the function sqrt returns a double. Functions can return values of any type. The library whose interface is specified in supplies many useful mathematical functions. Boolean expressions and tests have values of true or false and are used as the tests that guard the body of code in if/else statements. The type bool is a built-in type in C++ with values of true and false. A block (compound) statement is surrounded by { and } delimiters and is used to group several statements together. Relational operators are used to compare values. For example, 3<4is a relational expression using the < operator. Relational operators include ==, !=, <, >, <=, >=. Relational expressions have boolean values. Logical operators are used to combine boolean expressions. The logical operators are ||, &&, !. Both || and && (logical or and logical and, respectively) are evaluated using short-circuit evaluation. Boolean operators in C++ use short-circuit evaluation so that only as much of an expression is evaluated from left-to-right as needed to determine whether the expression is true (or false). Defensive programming is a style of programming in which care is taken to prevent errors from occurring rather than trying to clean up when they do occur. Pre- and postconditions are a method of commenting functions; if the preconditions are true when a function is called, the postconditions will be true when the function has finished executing. These provide a kind of contractual arrangement between a function and the caller of a function. Several member functions of the string class can be used to determine the length of a string and to find substrings of a given string. Non-member functions are called free functions. Functions encapsulate abstractions like when a leap year occurs and in calculating a square root. Functions should be used with regularity in programs. Classes encapsulate related functions together. The class string encapsulates functions related to manipulating strings and the class Date encapsulates functions related to calendar dates. De Morgan’s laws are useful in developing boolean expressions for use in if statements, and in reasoning about complex boolean expressions. June 7, 1999 10:10 owltex Sheet number 66 Page number 148 magenta black

148 Chapter 4 Control, Functions, and Classes 4.9 Exercises

4.1 Write a program that prompts the user for a person’s ﬁrst and last names (be careful; more than one cin >> statement may be necessary). The program should print a message that corresponds to the user’s names. The program should recognize at least four different names. For example:

OUTPUT

enter your first name> Owen enter your last name> Astrachan Hi Owen, your last name is interesting. enter your first name> Dave enter your last name> Reed Hi Dave, your last name rhymes with thneed.

4.2 Write a function whose speciﬁcation is string IntToRoman(int num) // precondition: 0 <= num <= 10 // postcondition: returns Roman equivalent of num so that cout << IntToRoman(7) << endl; would cause "VII" to be printed. Note the precondition. Write a program to test that the function works. 4.3 Write a function with prototype int Min2(int,int) that returns the minimum value of its parameters. Then use this function to write another function with prototype int Min3(int,int,int) that returns the minimum of its three parameters. Min3 can be written with a single line: int Min3(int x, int y, int z) // post: returns minimum of x, y, and z { return Min2( ); } where the two-parameter function is called with appropriate actual parameters. Write a test program to test both functions. You can then rewrite the minimum functions, naming them both Min. In C++, functions can have the same name, if their parameters differ (this is another example of overloading). 4.4 Write a program in which the user is prompted for a real number (of type double) and a positive integer and that prints the double raised to the integer power. Use the function pow from . For example: June 7, 1999 10:10 owltex Sheet number 67 Page number 149 magenta black

4.9 Exercises 149

OUTPUT

enter real number 3.5 enter positive power 5 3.5 raised to the power 5 = 525.218

4.5 Write a program that is similar to numtoeng.cpp, Program 4.1, but that prints an English equivalent for any number less than one million. If you know a language other than English (e.g., French, Spanish, Arabic), use that language instead of English. 4.6 Use the function sqrt from the math library13 to write a function PrintRoots that prints the roots of a quadratic equation whose coefﬁcients are passed as parameters. PrintRoots(1,-5,6); might cause the following to be printed, but your output doesn’t have to look exactly like this.

OUTPUT

roots of equation 1*xˆ2 - 5*x + 6 are 2.0 and 3.0

4.7 (from [Coo87]) The surface area of a person is given by the formula

7.184−3 × weight0.452 × height0.725 (4.2)

where weight is in kilograms and height is in centimeters. Write a program that prompts for height and weight and then prints the surface area of a person. Use the function pow from to raise a number to a power. 4.8 Write a program using the class Date that prints the day of the week on which your birthday occurs for the next seven years. 4.9 Write a program using ideas from the head-drawing program parts.cpp, Program 2.4, that could be used as a kind of police sketch program. A sample run could look like the following.

13On some systems you may need to link the math library to get access to the square root function. June 7, 1999 10:10 owltex Sheet number 68 Page number 150 magenta black

150 Chapter 4 Control, Functions, and Classes

OUTPUT

prompt> sketch Choices of hair style follow

(1) parted (2) brush cut (3) balding

enter choice: 1 Choices of eye style follow

(1) beady-eyed (2) wide-eyed (3) wears glasses

enter choice: 3 Choices of mouth style follow

(1) smiling (2) straightfaced (3) surprised

enter choice: 3

||||||||//////// || | ------| |---|o|--|o|---| | ------| _| |_ |_ _| |o| ||

4.10 Write a function that allows the user to design different styles of T-shirts. You should allow choices for the neck style, the sleeve style, and the phrase or logo printed on the T-shirt. For example, June 7, 1999 10:10 owltex Sheet number 69 Page number 151 magenta black

4.9 Exercises 151

OUTPUT

prompt> teedesign Choices of neck style follow

(1) turtle neck (2) scoop neck (rounded) (3) vee neck

enter choice: 1 Choices of sleeve style follow

(1) short (2) sleeveless (3) long

enter choice: 2 Choices of logo follow

(1) logo once (2) logo three times (3) logo slanted

enter choice: 3 +------+ || ------/\ /\ -- -- || || || -- -- |F | |O | |O| || ||

4.11 (from[KR96]) The wind chill temperature is given according to a somewhat complex formula derived empirically. The formula converts a temperature (in degrees Fahren- heit) and a wind speed to an equivalent temperature (eqt) as follows:   temp√ if wind ≤ 4 = a − (b + c × − d × ) × (a − )/e ≤ eqt  wind wind temp if temp 45 (4.3) 1.6 ∗ temp − 55.0 otherwise June 7, 1999 10:10 owltex Sheet number 70 Page number 152 magenta black

152 Chapter 4 Control, Functions, and Classes

Where a = 91.4,b = 10.45,c = 6.69,d = 0.447,e = 22.0. Write a program that prompts for a wind speed and a temperature and prints the corresponding wind chill temperature. Use a function WindChill with the following prototype: double WindChill(double temperature, double windSpeed) // pre: temperature in degrees Fahrenheit // post: returns wind-chill index/ // comparable temperature 4.12 (also from [KR96]) The U.S. CDC (Centers for Disease Control—this time, not Control Data Corporation) determine obesity according to a “body mass index,” computed by weight in kilograms index = (4.4) (height in meters)2 An index of 27.8 or greater for men or 27.3 or greater for nonpregnant women is considered obese. Write a program that prompts for height, weight, and sex and that determines whether the user is obese. Write a function that returns the body mass index given the height and weight in inches and pounds, respectively. Note that one meter is 39.37 inches, one inch is 2.54 centimeters, one kilogram is 2.2 pounds, and one pound is 454 grams. 4.13 Write a program that converts a string to its Pig-Latin equivalent. To convert a string to Pig-Latin use the following algorithm:

1. If the string begins with a vowel, add "way" to the string. For example, Pig-Latin for “apple” is “appleway.” 2. Otherwise, find the first occurrence of a vowel, move all the characters before the vowel to the end of the word, and add "ay". For example, Pig-Latin for “strong” is “ongstray” since the characters “str” occur before the first vowel.

Assume that vowels are a, e, i, o, and u. You’ll find it useful to write several functions to help in converting a string to its Pig-Latin equivalent. You’ll need to use string member functions substr, find, and length. You’ll also need to concatenate strings using +. Finally, to find the first vowel, you may find it useful to write a function that returns the minimum of two values. You’ll need to be careful with the value string::npos returned by the string member function find. Sample output for the program follows.

OUTPUT

prompt> pigify enter string: strength strength = engthstray prompt> pigify enter string: alpha alpha = alphaway prompt> pigify enter string: frzzl frzzl = frzzlay